Dirac Equation
The Dirac equation, published by Paul Dirac in 1928, is the relativistic wave equation for spin-½ particles such as the Electron.
The standard account
Dirac sought a wave equation first order in time, as Quantum Mechanics requires, and also first order in space, as Special Relativity symmetry suggests. Meeting both conditions forced him to introduce four anticommuting matrices and a four-component wave function — the bispinor. Three results followed with no further assumptions:
- Spin. Electron spin of one-half, previously inserted by hand, emerges from the structure of the equation, together with the gyromagnetic ratio g = 2 (the small deviation from 2 is a quantum-electrodynamic effect, calculated and measured to more than ten digits).
- Fine structure. The equation reproduces the fine structure of the Hydrogen Atom spectrum correctly.
- Antimatter. The equation has negative-energy solutions. Dirac's interpretation — a filled "sea" of negative-energy states whose holes appear as positive particles of opposite charge — predicted the positron, which Carl Anderson observed in cosmic rays in 1932.
In modern quantum field theory the negative-energy sea is dropped: the Dirac field is quantised, and the antiparticle appears as a distinct excitation. The equation remains the foundation of relativistic quantum mechanics and of the electron sector of the Standard Model.
On this wiki
The Dirac equation is invoked constantly in the quantum-alternative literature catalogued here, generally by authors seeking a deterministic or classical reading of what the bispinor describes.
- Robert A Close's A Dirac Equation (2008) argues that the equation is fundamentally deterministic — an evolution equation for angular momentum density — and shows that a classical second-order wave equation for angular momentum density in an elastic solid is equivalent to a bispinor equation. He argues the conventional parity operator is derived incorrectly, and that wave interference in this reading produces both the Lorentz force and the Pauli Exclusion Principle.
- Don L Hotson's Dirac's Equation and the Sea of Negative Energy, Part 1 and its sequel argue that the negative-energy sea was discarded prematurely and that much of modern physics has been built around the omission.
- Peter Rowlands approaches the equation algebraically in Breaking the Dirac Code, deriving particle structure from a nilpotent formulation.
- Milo M Wolff and others in Category:Quantum Theory pursue wave-structure-of-matter readings of electron spin.
- Genuine Subharmonic Equations to Replace Those of Schrödinger and Dirac proposes replacements outright.
Common to most of these is not a claim that the equation's predictions are wrong — they are among the best confirmed in physics — but the claim that its probabilistic interpretation is optional, and that a physical wave in a medium underlies it.